Not yet reviewed by Pith; the record is open.

Materials that are lightweight yet exhibit superior mechanical properties are of compelling importance for several technological applications that range from aircrafts to household appliances. Lightweight materials allow energy saving and reduce the amount of resources required for manufacturing. Researchers have expended significant efforts in the quest for such materials, which require new concepts in both tailoring material microstructure as well as structural design. Architectured materials, which take advantage of new engineering paradigms, have recently emerged as an exciting avenue to create bespoke combinations of desired macroscopic material responses. In some instances, rather unique structures have emerged from advanced geometrical concepts (e.g. gyroids, menger cubes, or origami/kirigami-based structures), while in others innovation has emerged from mimicking nature in bio-inspired materials (e.g. honeycomb structures, nacre, fish scales etc.). Beyond design, additive manufacturing has enabled the facile fabrication of complex geometrical and bio-inspired architectures, using computer aided design models. The combination of simulations and experiments on these structures has led to an enhancement of mechanical properties, including strength, stiffness and toughness. In this review, we provide a perspective on topologically engineered architectured materials that exhibit optimal mechanical behaviour and can be readily printed using additive manufacturing.